Problem 1 - PLEASE SHOW WORK

A bank has the following simple balance sheet: Assets Liabilities Loans (L) Deposits (D) Government Bond (G) Net Worth (K) D = -800 + 20000*RD ; L = 1000 10000*RL; RG = 6% Here, D is the amount of deposit funds supplied to the bank and RD is the rate of interest offered; L is the dollar volume of loans demanded and RL is the interest rate charged on loans; RG is the rate of return for government bonds.

(1) Determine the optimal D* and L* so the bank will generate maximum profit.

(2) Calculate the banks profit if K = 50.